Shape Optimization Design for a Centrifuge Structure with Multi Topological Configurations Based on the B-Spline FCM and GCMMA

Round 1

Reviewer 1 Report

The article presents shape optimization of a structural component that undergoes centrifugal loading. The authors use B-spline finite cell method for the analysis and a gradient-based optimization method to reduce mass, with a maximum stress constraint. The proposed design method is demonstrated to perform well in the four examples provided. The unique contribution of this work seems to be the application of shape optimization for a problem with complex loading and its handling through B-spline FCM, however, this is not clear or emphasized enough. Clarifications of some of the method descriptions and discussions, as suggested below, would improve the quality of the article further.

Major revisions:

The main contributions of the work are stated in lines 76-80, however, the implications on the broader impact of the presented method are not included in those statements, making the contributions seem very specific. To make a stronger case, the authors should include a brief description of unique challenges of shape optimization of the basket of geotechnical centrifuge, as discussed in a couple of paragraphs leading up to this. Line 46: the term “basket” should be defined (describe what it is concisely) for those who are not familiar with geotechnical centrifuges, before start describing the requirements. Use of Fig.1 here may be helpful. The description of how the level set function relates to the lifting lug model with R-functions is not clear. Where does phi show up in the equilibrium equation, and how is it related to the design variables? How is dphi/dd compute? Please provide more explanations. Please describe what refinement criteria are used for the octree cell generation, around line 131. Please provide more information regarding how the Dirichlet BCs are applied, around line 136-138. Line 164: please clarify what is meant by “experimental model” – does this refer to a mathematical model of some sort, or some component used for experiments? In the conclusion section, offer comments on how the proposed method could be applied to other problems or on any future works. In the abstract, instead of simply referring to the best result as “case 4”, use descriptive words so that the readers have enough information to understand what this means before reading the article.

Minor revisions:

Line 170: remove the indentation at the beginning. Line 172: symbol “H” should be reserved for the Heaviside function – use a different symbol for the width. Line 194: a symbol other than “d” should be used here, if both y's and d's are meant to be included in this vector. Line 271: “maximum increasing by …” should be “maximum stress increasing by …” The term used to refer to “m” (for example in Eq.(3)) should be expressed as mass, not quality. Please make corrections throughout the document. Some spaces after periods are missing. Please check throughout the document. Please use larger fonts for texts inserted in figures.

Author Response

Dear Editors and Reviewers,

We appreciate your consideration of our paper and the reviewers’ constructive comments and suggestions. We have made a thorough revision of our paper accordingly, and detailed replies to the reviewers’ comments are listed in the attachment. All the modifications have been highlighted in the revised paper.

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript deals with the shape design of the basket of a geotechnical centrifuge, describing the design procedure and one example.
The shape design is based on a parameterization of the basket geometry coupled with a B-Spline Finite Cell Method (FCM). The shape parameterization is based on a Level Set Method that is in turn based on the R-functions.
The proposed application is related to the optimization of the basket aiming at the minimization of its weight, subjected to stress constraints computed by a FCM analysis.
The main issue is the odd structure. It is not entirely clear what we are looking at. Is this a generic methodology or is it a one-off design study? The main contributions listed in the introduction section, the generic-looking flowcharts of Figure 8, etc. would suggest the former, but the rather convoluted single application suggests the latter. If the former is the case, one would expect a clear methods section, followed by a series of applications (not just a single basket), presented in a concise, high level fashion. What we have instead is that the part of the paper that describes the case study has elements of 'method' mixed in with the results of the particular analysis case. Much of the detail there could be in an appendix and the methodology/formulations part should be promoted to the methods part of the paper. If the authors are claiming a general methodology, that needs to be illustrated with a range of examples, its limitations specified, benchmarked, etc. Otherwise, if the methodology only works for this specific case, I can not see any innovative aspect in the specific application that, at the end, is only the optimization of a geotechnical centrifuge. In this last case, I can not suggest the publication of the paper.

Some specific comments:

The authors often repeat through the text that the "stress are considered as design variables". This is not true and makes it seems that the authors do not know what they wrote because, in the optimization problem definition, the stress is a constraint.

It is not clear at all how the level set method is used and how it is coupled with the geometry definition and to the FCM model generation. Moreover, how the design variables represented in Figure 5 are related to the the level set method? Frankly speaking, they actually look like CAD parameters instead of the parameters of a level set method. These aspects must be improved more than anything else.
Concerning the level set method, Figure 2 (a and b) were extracted in internet. I want to remind the authors that a scientific manuscript must be completely original.

Concerning the basket application, fundamental information is completely missing. One for all: what is the material that it is made of? This is very important in order to understand something more about the maximum stress used as constraint inside the optimization.

Author Response

Dear Editors and Reviewers, We appreciate your consideration of our paper and the reviewers’ constructive comments and suggestions. We have made a thorough revision of our paper accordingly, and detailed replies to the reviewers’ comments are listed in the attachment. All the modifications have been highlighted in the revised paper. Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Authors improved the manuscript taking into account the comments provided by the reviewers. Thank you for this.

I think there is only one innovative aspect in the paper: the sensitivity analysis coupled with the shape optimization via the FCM.

For this reason I can suggest the publication of the paper in the present form.